The first volume of the proceedings of the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) covers topics that include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers, as well as the reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods. Altogether, a rather comprehensive overview is given of the state of the art in the field.

The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications.

Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations."

"Mathematical Concepts and Methods in Modern Biology" offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology.

Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software.
Features self-contained chapters with real biological research examples using freely available computational toolsSpans several mathematical techniques at basic to advanced levelsOffers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology"

This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.

This volume developed from a Workshop on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding which was held at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, from June 1-5, 2010. The subject matter ranged widely from observational data to theoretical mechanics, and reflected the broad scope of the workshop. In both the prepared presentations and in the informal discussions, the workshop engaged exchanges across disciplines and invited a lively interaction between modelers and observers. The articles in this volume were invited and fully refereed. They provide a representative if necessarily incomplete account of the field of natural locomotion during a period of rapid growth and expansion. The papers presented at the workshop, and the contributions to the present volume, can be roughly divided into those pertaining to swimming on the scale of marine organisms, swimming of microorganisms at low Reynolds numbers, animal flight, and sliding and other related examples of locomotion.

Vortices comprising swirling motion of matter are observable in classical systems at all scales ranging from atomic size to the scale of galaxies. In quantum mechanical systems, such vortices are robust entities whose behaviours are governed by the strict rules of topology. The physics of quantum vortices is pivotal to basic science of quantum turbulence and high temperature superconductors, and underpins emerging quantum technologies including topological quantum computation. This handbook is aimed at providing a dictionary style portal to the fascinating quantum world of vortices.

The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any "a priori" assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in "H"1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.

In the nonlinear case, again after "ad hoc" scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Karman equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.

This book introduces the fascinating world of plasmonics and physics at the nanoscale, with a focus on simulations and the theoretical aspects of optics and nanotechnology. A research field with numerous applications, plasmonics bridges the gap between the micrometer length scale of light and the secrets of the nanoworld. This is achieved by binding light to charge density oscillations of metallic nanostructures, so-called surface plasmons, which allow electromagnetic radiation to be focussed down to spots as small as a few nanometers. The book is a snapshot of recent and ongoing research and at the same time outlines our present understanding of the optical properties of metallic nanoparticles, ranging from the tunability of plasmonic resonances to the ultrafast dynamics of light-matter interaction. Beginning with a gentle introduction that highlights the basics of plasmonic interactions and plasmon imaging, the author then presents a suitable theoretical framework for the description of metallic nanostructures. This model based on this framework is first solved analytically for simple systems, and subsequently through numerical simulations for more general cases where, for example, surface roughness, nonlinear and nonlocal effects or metamaterials are investigated.

Der Grundkurs Theoretische Physik deckt in 7 Banden alle fur das Diplom und fur Bachelor/Master-Studiengange massgeblichen Gebiete ab. Jeder Band vermittelt das im jeweiligen Semester notwendige theoretisch-physikalische Rustzeug. UEbungsaufgaben mit ausfuhrlichen Loesungen dienen der Vertiefung des Stoffs. Der 4. Band behandelt die Gebiete Thermodynamik und Relativitatstheorie. Fur die Neuauflage wurde er grundlegend uberarbeitet und um 24 Aufgaben erganzt. Durch die zweifarbige Gestaltung ist der Stoff jetzt noch ubersichtlicher gegliedert.

The author develops a new perturbative formalism of non-equilibrium thermal quantum field theory for non-homogeneous backgrounds. As a result of this formulation, the author is able to show how so-called pinch singularities can be removed, without resorting to ad hoc prescriptions, or effective resummations of absorptive effects. Thus, the author arrives at a diagrammatic approach to non-equilibrium field theory, built from modified Feynman rules that are manifestly time-dependent from tree level. This new formulation provides an alternative framework in which to derive master time evolution equations for physically meaningful particle number densities, which are valid to all orders in perturbation theory and to all orders in gradient expansion. Once truncated in a loop-wise sense, these evolution equations capture non-equilibrium dynamics on all time-scales, systematically describing energy-violating processes and the non-Markovian evolution of memory effects

This book offers a comprehensive treatment of nonlocal elasticity theory as applied to the prediction of the mechanical characteristics of various types of biological and non-biological nanoscopic structures with different morphologies and functional behaviour. It combines fundamental notions and advanced concepts, covering both the theory of nonlocal elasticity and the mechanics of nanoscopic structures and systems. By reporting on recent findings and discussing future challenges, the book seeks to foster the application of nonlocal elasticity based approaches to the emerging fields of nanoscience and nanotechnology. It is a self-contained guide, and covers all relevant background information, the requisite mathematical and computational techniques, theoretical assumptions, physical methods and possible limitations of the nonlocal approach, including some practical applications. Mainly written for researchers in the fields of physics, biophysics, mechanics, and nanoscience, as well as computational engineers, the book can also be used as a reference guide for senior undergraduate and graduate students, as well as practicing engineers working in a range of areas, such as computational condensed matter physics, computational materials science, computational nanoscience and nanotechnology, and nanomechanics.

Ge and III-V compounds, semiconductors with high carrier mobilities, are candidates to replace Si as the channel in MOS devices. 2D materials - like graphene and MoS_2 - are also envisioned to replace Si in the future. This thesis is devoted to the first-principles modeling of the vibrational properties of these novel channel materials. The first part of the thesis focuses on the vibrational properties of various oxides on Ge, making it possible to identify the vibrational signature of specific defects which could hamper the proper functioning of MOSFETs. The second part of the thesis reports on the electronic and vibrational properties of novel 2D materials like silicene and germanene, the Si and Ge 2D counterparts of graphene. The interaction of these 2D materials with metallic and non-metallic substrates is investigated. It was predicted, for the first time, and later experimentally confirmed, that silicene could be grown on a non-metallic template like MoS_2, a breakthrough that could open the door to the possible use of silicene in future nanoelectronic devices.

Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.

This book describes five qualitative investment decision-making methods based on the hesitant fuzzy information. They are: (1) the investment decision-making method based on the asymmetric hesitant fuzzy sigmoid preference relations, (2) the investment decision-making method based on the hesitant fuzzy trade-off and portfolio selection, (3) the investment decision-making method based on the hesitant fuzzy preference envelopment analysis, (4) the investment decision-making method based on the hesitant fuzzy peer-evaluation and strategy fusion, and (5) the investment decision-making method based on the EHVaR measurement and tail analysis.

This book explores the rise of theoretical physics in 19th century Germany. The authors show how the junior second physicist in German universities over time became the theoretical physicist, of equal standing to the experimental physicist. Gustav Kirchhoff, Hermann von Helmholtz, and Max Planck are among the great German theoretical physicists whose work and career are examined in this book. Physics was then the only natural science in which theoretical work developed into a major teaching and research specialty in its own right. Readers will discover how German physicists arrived at a well-defined field of theoretical physics with well understood and generally accepted goals and needs. The authors explain the nature of the work of theoretical physics with many examples, taking care always to locate the research within the workplace. The book is a revised and shortened version of Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, a two-volume work by the same authors. This new edition represents a reformulation of the larger work. It retains what is most important in the original work, while including new material, sharpening discussions, and making the research more accessible to readers. It presents a thorough examination of a seminal era in physics.

The purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion.
Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures.
End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book."

Starting from fundamentals of classical stability theory, an overview is given of the transition phenomena in subsonic, wall-bounded shear flows. At first, the consideration focuses on elementary small-amplitude velocity perturbations of laminar shear layers, i.e. instability waves, in the simplest canonical configurations of a plane channel flow and a flat-plate boundary layer. Then the linear stability problem is expanded to include the effects of pressure gradients, flow curvature, boundary-layer separation, wall compliance, etc. related to applications. Beyond the amplification of instability waves is the non-modal growth of local stationary and non-stationary shear flow perturbations which are discussed as well. The volume continues with the key aspect of the transition process, that is, receptivity of convectively unstable shear layers to external perturbations, summarizing main paths of the excitation of laminar flow disturbances. The remainder of the book addresses the instability phenomena found at late stages of transition. These include secondary instabilities and nonlinear features of boundary-layer perturbations that lead to the final breakdown to turbulence. Thus, the reader is provided with a step-by-step approach that covers the milestones and recent advances in the laminar-turbulent transition. Special aspects of instability and transition are discussed through the book and are intended for research scientists, while the main target of the book is the student in the fundamentals of fluid mechanics. Computational guides, recommended exercises, and PowerPoint multimedia notes based on results of real scientific experiments supplement the monograph. These are especially helpful for the neophyte to obtain a solid foundation in hydrodynamic stability. To access the supplementary material go to extras.springer.com and type in the ISBN for this volume.

This volume presents the state-of-the-art in selected topics across modern nuclear physics, covering fields of central importance to research and illustrating their connection to many different areas of physics. It describes recent progress in the study of superheavy and exotic nuclei, which is pushing our knowledge to ever heavier elements and neutron-richer isotopes. Extending nuclear physics to systems that are many times denser than even the core of an atomic nucleus, one enters the realm of the physics of neutron stars and possibly quark stars, a topic that is intensively investigated with many ground-based and outer-space research missions as well as numerous theoretical works. By colliding two nuclei at very high ultra-relativistic energies one can create a fireball of extremely hot matter, reminiscent of the universe very shortly after the big bang, leading to a phase of melted hadrons and free quarks and gluons, the so-called quark-gluon plasma. These studies tie up with effects of crucial importance in other fields. During the collision of heavy ions, electric fields of extreme strength are produced, potentially destabilizing the vacuum of the atomic physics system, subsequently leading to the decay of the vacuum state and the emission of positrons. In neutron stars the ultra-dense matter might support extremely high magnetic fields, far beyond anything that can be produced in the laboratory, significantly affecting the stellar properties. At very high densities general relativity predicts the stellar collapse to a black hole. However, a number of current theoretical activities, modifying Einstein's theory, point to possible alternative scenarios, where this collapse might be avoided. These and related topics are addressed in this book in a series of highly readable chapters. In addition, the book includes fundamental analyses of the practicalities involved in transiting to an electricity supply mainly based on renewable energies, investigating this scenario less from an engineering and more from a physics point of view. While the topics comprise a large scope of activities, the contributions also show an extensive overlap in the methodology and in the analytical and numerical tools involved in tackling these diverse research fields that are the forefront of modern science.

The main body of this book is devoted to statistical physics, whereas much less emphasis is given to thermodynamics. In particular, the idea is to present the most important outcomes of thermodynamics - most notably, the laws of thermodynamics - as conclusions from derivations in statistical physics. Special emphasis is on subjects that are vital to engineering education. These include, first of all, quantum statistics, like the Fermi-Dirac distribution, as well as diffusion processes, both of which are fundamental to a sound understanding of semiconductor devices. Another important issue for electrical engineering students is understanding of the mechanisms of noise generation and stochastic dynamics in physical systems, most notably in electric circuitry. Accordingly, the fluctuation-dissipation theorem of statistical mechanics, which is the theoretical basis for understanding thermal noise processes in systems, is presented from a signals-and-systems point of view, in a way that is readily accessible for engineering students and in relation with other courses in the electrical engineering curriculum, like courses on random processes.

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.

This book, authored by a well-known researcher and expositor in meteorology, focuses on the direct link between molecular dynamics and atmospheric variation. Uniting molecular dynamics, turbulence theory, fluid mechanics and non equilibrium statistical mechanics, it is relevant to the fields of applied mathematics, physics and atmospheric sciences, and focuses on fluid flow and turbulence, as well as on temperature, radiative transfer and chemistry. With extensive references and glossary this is an ideal text for graduates and researchers in meteorology, applied mathematics and physical chemistry.

This book provides a comprehensive overview of the theoretical concepts and experimental applications of planar waveguides and other confined geometries, such as optical fibres. Covering a broad array of advanced topics, it begins with a sophisticated discussion of planar waveguide theory, and covers subjects including efficient production of planar waveguides, materials selection, nonlinear effects, and applications including species analytics down to single-molecule identification, and thermo-optical switching using planar waveguides. Written by specialists in the techniques and applications covered, this book will be a useful resource for advanced graduate students and researchers studying planar waveguides and optical fibers.

This book looks at the increasing interest in running microscopy processing algorithms on big image data by presenting the theoretical and architectural underpinnings of a web image processing pipeline (WIPP). Software-based methods and infrastructure components for processing big data microscopy experiments are presented to demonstrate how information processing of repetitive, laborious and tedious analysis can be automated with a user-friendly system. Interactions of web system components and their impact on computational scalability, provenance information gathering, interactive display, and computing are explained in a top-down presentation of technical details. Web Microanalysis of Big Image Data includes descriptions of WIPP functionalities, use cases, and components of the web software system (web server and client architecture, algorithms, and hardware-software dependencies). The book comes with test image collections and a web software system to increase the reader's understanding and to provide practical tools for conducting big image experiments. By providing educational materials and software tools at the intersection of microscopy image analyses and computational science, graduate students, postdoctoral students, and scientists will benefit from the practical experiences, as well as theoretical insights. Furthermore, the book provides software and test data, empowering students and scientists with tools to make discoveries with higher statistical significance. Once they become familiar with the web image processing components, they can extend and re-purpose the existing software to new types of analyses. Each chapter follows a top-down presentation, starting with a short introduction and a classification of related methods. Next, a description of the specific method used in accompanying software is presented. For several topics, examples of how the specific method is applied to a dataset (parameters, RAM requirements, CPU efficiency) are shown. Some tips are provided as practical suggestions to improve accuracy or computational performance.

This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality. Written in a didactic style, this book includes many examples and solved exercises. The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras. This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.

The primary objective of this book is to study some of the research topics in the area of analysis of complex surveys which have not been covered in any book yet. It discusses the analysis of categorical data using three models: a full model, a log-linear model and a logistic regression model. It is a valuable resource for survey statisticians and practitioners in the field of sociology, biology, economics, psychology and other areas who have to use these procedures in their day-to-day work. It is also useful for courses on sampling and complex surveys at the upper-undergraduate and graduate levels. The importance of sample surveys today cannot be overstated. From voters' behaviour to fields such as industry, agriculture, economics, sociology, psychology, investigators generally resort to survey sampling to obtain an assessment of the behaviour of the population they are interested in. Many large-scale sample surveys collect data using complex survey designs like multistage stratified cluster designs. The observations using these complex designs are not independently and identically distributed - an assumption on which the classical procedures of inference are based. This means that if classical tests are used for the analysis of such data, the inferences obtained will be inconsistent and often invalid. For this reason, many modified test procedures have been developed for this purpose over the last few decades.